Theorem necon2bi

Description: Contrapositive inference for inequality. (Contributed by NM, 1-Apr-2007)

	Ref	Expression
Hypothesis	necon2bi.1	⊢ ( 𝜑 → 𝐴 ≠ 𝐵 )
Assertion	necon2bi	⊢ ( 𝐴 = 𝐵 → ¬ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		necon2bi.1	⊢ ( 𝜑 → 𝐴 ≠ 𝐵 )
2	1	neneqd	⊢ ( 𝜑 → ¬ 𝐴 = 𝐵 )
3	2	con2i	⊢ ( 𝐴 = 𝐵 → ¬ 𝜑 )